Keen to open a discussion around the subject of "reading the rock" and wish to invite as many climbers as possible to participate, especially the ones at the top of the game.

I'm fascinated by this all-important climber's attribute. Some have it more than others and seem to glide up routes on-sight, never wasting time figuring out the most efficient move or sequence of moves. I'm curious to know how important climbers rate this attribute compared to others such as strength / stamina, composure / nerve, daring, technique and being comfortable high off the ground. Also, are there anything a climber can do to improve his / her ability to read the rock, other than climbing? And can anyone shed light on what exactly it is (in the brain) that makes some climbers read rock at a glance while others have to stare at it for a while before linking a sequence of moves together that even then turns out to be inefficient?

It's quite simple. Reading routes comes from experience and experience is most easily gained by bouldering.

As climbing is about "the flowing movement" as you said, this flowing is allowed by muscle memory. Doing a great diversity of movements while bouldering allows for a great diversity of movements when out on rocks. If you want to make flowing easier quickly, work on your locking off ability and finger strength, but easier just to boulder a lot to gain diversity.

Locking off allows a climber to clip easier, making the next movements less strenuous and mentally easier. Finger strength allows you to hold on when your arms get tired or when you execute a sequence incorrectly and you have to hold onto smaller holds to get to the big ones and also confidence when you grab anything that you can keep pulling.

Lastly, if you wanna flow, learn to fall. Whether you bouldering, tradding or sport climbing, you need to let go of whats keeping you from focusing on the climb. Climbing is way easier if you have already accepted that you may take a 10m wipper and you will be fine.

Last lastly, learn to use your feet and look for feet placements while your climbing up. Your feet can hold most your weight if you use them correctly. A lot of people will say that shoes don't matter. They do. There only 2 shoe brands I rate in South Africa and I chose to represent 5.10 as stealth rubber sticks to anything. Using your shoes while bouldering is key as you learn to use your feet in different ways as to maximize your movement ability.

All advice above is my own and applies to you whether you a fast or slow climber. Climb at your own pace and learn that you have your own style, dont force what others can do, learn what you best at and conquer with it.

I think climbing routes below your maximum grade is a good way of learing the flow. If you aren't scratching and clawing your way to redpointing the next big number all the time you get chance to relax and move with ease, rather than it all being a stressed out tussle. Also redoing routes harder you have done before with (as Ebert says) the acceptance that you may well fall and not trying to "tick" it again and experimenting with different ways of doing the same moves can be useful.

1) climb [lots]
2) think about what you're doing. Even if you are repeating an old favourite, try different sequences. Think tactics, foot work and body position.
3) Keep an open mind. What may seem impossible / weird may work well
4) Watch your mates, hotshots and videos. (a true master has the humility to learn from his students)